Flutter inhibiting intake for gas turbine propulsion system

ABSTRACT

Disclosed is flutter damper including a first cavity having a radially inner side in fluid communication with a flow path, and a second cavity having a radially inner side in fluid communication with a radially outer side of the first cavity, and the flutter damper having an impedance characteristic at one or more target frequencies defined as
 
 f   target   =f   S,ND   +Ω·ND  
         wherein f S,ND  is a resonance frequency corresponding to a structural mode of a rotating component, ND is a nodal diameter count of the structural mode, and Ω is a rotational speed of the rotating component, and wherein the flutter damper has the following impedance characteristic at the one or more targeted frequencies
 
 R ≥2ρ c  
 
−3ρ c≤X ≤−0.6ρ c  
   wherein R is the real part of the impedance characteristic, X is the imaginary part of the impedance characteristic, ρ is air density, and c is speed of sound.

BACKGROUND

Exemplary embodiments pertain to flutter dampers in gas turbinepropulsion systems and, more particularly, to flutter dampers in nacelleinlet structures.

Geared turbofan architectures, allow for high bypass ratio turbofans,enabling the use of low pressure ratio fans, which may be moresusceptible to fan flutter than high pressure ratio fans. Fan flutter isan aeromechanical instability detrimental to the life of a fan blade.

Accordingly, there is a need for a flutter damper which, by absorbingthe acoustic energy associated with the flutter structural mode, mayprevent the fan from fluttering, and which may be integrated into thereduced available space in an optimized propulsion system.

BRIEF DESCRIPTION

Disclosed is flutter damper including a first cavity having a radiallyinner side in fluid communication with a flow path, and a second cavityhaving a radially inner side in fluid communication with a radiallyouter side of the first cavity, and the flutter damper having animpedance characteristic at one or more target frequencies defined asf _(target) =f _(S,ND) +Ω·NDwherein f_(S,ND) is a resonance frequency corresponding to a structuralmode of a rotating component, ND is a nodal diameter count of thestructural mode, and Ω is a rotational speed of the rotating component,and wherein the flutter damper has the following impedancecharacteristic at the one or more targeted frequenciesR≥2ρc−3ρc≤X≤−0.6ρcwherein R is the real part of the impedance characteristic, X is theimaginary part of the impedance characteristic, ρ is air density, and cis speed of sound.

In addition to one or more of the features described above, or as analternative, further embodiments may include that the rotating componentis a fan blade, and the targeted frequencies include

-   -   f_(S,ND)=frequency of first or second bending mode of fan with        ND nodal diameters        1≤ND≤3        Ω_(Mreltip=0.85)≤Ω≤Ω_(Mreltip=1.2)        wherein Mreltip is a relative Mach number for a radial outer tip        of the fan blade, and the bending mode is a vibrational mode of        the fan blade.

In addition to one or more of the features described above, or as analternative, further embodiments may include that at the one or moretarget frequencies:

$0.0143 \leq \frac{{Vf}_{target}}{Sc} \leq 0.165$wherein V is a combined volume of the first and second cavities, and Sis an entrance area to the second cavity.

In addition to one or more of the features described above, or as analternative, further embodiments may include that the first cavity andthe flow path surface fluidly communicate through a first perforatedsurface, and the first cavity and second cavity fluidly communicatethrough a second perforated surface.

In addition to one or more of the features described above, or as analternative, further embodiments may include that the first cavitycontains a cellular structure.

In addition to one or more of the features described above, or as analternative, further embodiments may include that the first cavity has asmaller volume than the second cavity.

In addition to one or more of the features described above, or as analternative, further embodiments may include that the first cavity is anacoustic liner for a propulsion system.

Further disclosed is a gas turbine engine system, including a nacelle,and a flutter damper disposed within the nacelle. The flutter damper mayinclude one or more of the above disclosed features.

Further disclosed is a method of providing flutter damping to a gasturbine engine, including passing a flow over a flutter damper having afirst cavity with a radially inner side in fluid communication with aflow path surface, and a second cavity having a radially inner side influid communication with a radially outer side of the first cavity, anddampening flutter for a rotating component disposed in a flow path withthe flutter damper at one or more target frequencies defined asf _(target) =f _(S,ND) +Ω·NDwherein f_(S,ND) is a resonance frequency corresponding to a structuralmode of the rotating component, ND is a nodal diameter count of thestructural mode, and Ω is a rotational speed of the rotating component,and wherein the flutter damper has the following impedancecharacteristic at the one or more targeted frequenciesR≥2ρc−3ρc≤X≤−0.6ρcwherein R is the real part of the impedance characteristic, X is theimaginary part of the impedance characteristic, ρ is air density, and cis speed of sound.

BRIEF DESCRIPTION OF THE DRAWINGS

The following descriptions should not be considered limiting in any way.With reference to the accompanying drawings, like elements are numberedalike:

FIG. 1 is a schematic view of a gas turbine propulsion system;

FIG. 2 illustrates a perspective cross sectional view of a flutterdamper in a nacelle inlet;

FIG. 3 is a schematic view of a flutter damper in accordance with oneembodiment of the disclosure;

FIGS. 4A and 4B illustrate perspective views of one chamber of a flutterdamper in accordance with one embodiment of the disclosure;

FIG. 5 illustrates an array of chambers of flutter dampers integratedinto the nacelle inlet;

FIG. 6 is a perspective view of a portion of the nacelle inlet;

FIG. 7 illustrates another schematic view of a gas turbine propulsionsystem with a flutter damper in accordance with one embodiment of thedisclosure; and

FIGS. 8A, 8B, and 8C illustrate flutter dampers in accordance withadditional embodiments of the disclosure.

DETAILED DESCRIPTION

A detailed description of one or more embodiments of the disclosedapparatus and method are presented herein by way of exemplification andnot limitation with reference to the Figures.

FIG. 1 schematically illustrates a gas turbine engine 20. The gasturbine engine 20 is disclosed herein as a two-spool turbofan thatgenerally incorporates a fan section 22, a compressor section 24, acombustor section 26 and a turbine section 28. Alternative engines mightinclude an augmentor section (not shown) among other systems orfeatures. The fan section 22 drives air along a bypass flow path B in abypass duct, while the compressor section 24 drives air along a coreflow path C for compression and communication into the combustor section26 then expansion through the turbine section 28. Although depicted as atwo-spool turbofan gas turbine engine in the disclosed non-limitingembodiment, it should be understood that the concepts described hereinare not limited to use with two-spool turbofans as the teachings may beapplied to other types of turbine engines including three-spoolarchitectures.

The exemplary engine 20 generally includes a low speed spool 30 and ahigh speed spool 32 mounted for rotation about an engine centrallongitudinal axis A relative to an engine static structure 36 viamultiple bearing systems 38. It should be understood that variousbearing systems 38 at various locations may alternatively oradditionally be provided, and the location of bearing systems 38 may bevaried as appropriate to the application.

The low speed spool 30 generally includes an inner shaft 40 thatinterconnects a fan 42, a low pressure compressor 44 and a low pressureturbine 46. The inner shaft 40 is connected to the fan 42 through aspeed change mechanism, which in exemplary gas turbine engine 20 isillustrated as a geared architecture 48 to drive the fan 42 at a lowerspeed than the low speed spool 30. The high speed spool 32 includes anouter shaft 50 that interconnects a high pressure compressor 52 and highpressure turbine 54. A combustor 56 is arranged in exemplary gas turbine20 between the high pressure compressor 52 and the high pressure turbine54. An engine static structure 36 is arranged generally between the highpressure turbine 54 and the low pressure turbine 46. The engine staticstructure 36 further supports bearing systems 38 in the turbine section28. The inner shaft 40 and the outer shaft 50 are concentric and rotatevia bearing systems 38 about the engine central longitudinal axis Awhich is collinear with their longitudinal axes.

The core airflow is compressed by the low pressure compressor 44 thenthe high pressure compressor 52, mixed and burned with fuel in thecombustor 56, then expanded over the high pressure turbine 54 and lowpressure turbine 46. The turbines 46, 54 rotationally drive therespective low speed spool 30 and high speed spool 32 in response to theexpansion. It will be appreciated that each of the positions of the fansection 22, compressor section 24, combustor section 26, turbine section28, and fan drive gear system 48 may be varied. For example, gear system48 may be located aft of combustor section 26 or even aft of turbinesection 28, and fan section 22 may be positioned forward or aft of thelocation of gear system 48.

The engine 20 in one example is a high-bypass geared aircraft engine. Ina further example, the engine 20 bypass ratio is greater than about six(6), with an example embodiment being greater than about ten (10), thegeared architecture 48 is an epicyclic gear train, such as a planetarygear system or other gear system, with a gear reduction ratio of greaterthan about 2.3 and the low pressure turbine 46 has a pressure ratio thatis greater than about five. In one disclosed embodiment, the engine 20bypass ratio is greater than about ten (10:1), the fan diameter issignificantly larger than that of the low pressure compressor 44, andthe low pressure turbine 46 has a pressure ratio that is greater thanabout five 5:1. Low pressure turbine 46 pressure ratio is pressuremeasured prior to inlet of low pressure turbine 46 as related to thepressure at the outlet of the low pressure turbine 46 prior to anexhaust nozzle. The geared architecture 48 may be an epicycle geartrain, such as a planetary gear system or other gear system, with a gearreduction ratio of greater than about 2.3:1. It should be understood,however, that the above parameters are only exemplary of one embodimentof a geared architecture engine and that the present disclosure isapplicable to other gas turbine engines including direct driveturbofans.

A significant amount of thrust is provided by the bypass flow B due tothe high bypass ratio. The fan section 22 of the engine 20 is designedfor a particular flight condition—typically cruise at about 0.8 Mach andabout 35,000 feet (10,688 meters). The flight condition of 0.8 Mach and35,000 ft (10,688 meters), with the engine at its best fuelconsumption—also known as “bucket cruise Thrust Specific FuelConsumption (‘TSFC’)”—is the industry standard parameter of lbm of fuelbeing burned divided by lbf of thrust the engine produces at thatminimum point. “Low fan pressure ratio” is the pressure ratio across thefan blade alone, without a Fan Exit Guide Vane (“FEGV”) system. The lowfan pressure ratio as disclosed herein according to one non-limitingembodiment is less than about 1.45. “Low corrected fan tip speed” is theactual fan tip speed in ft/sec divided by an industry standardtemperature correction of [(Tram ° R)/(518.7° R)]^(0.5). The “Lowcorrected fan tip speed” as disclosed herein according to onenon-limiting embodiment is less than about 1150 ft/second (350.5 m/sec).

As illustrated in FIGS. 1 through 3, the engine 20 may include a nacelle100 with acoustic liner 101 at the radial inside of the nacelle inletskin 106. The acoustic liner 101 may have a perforated radial inner facesheet 108, i.e., facing a radial inside of a nacelle inlet 103,illustrated in FIG. 2, and a radial outer back sheet 110.

The acoustic liner 101 is designed to absorb energy that tends toproduce community noise. As such, for contemporary high bypass ratiopropulsion systems, the acoustic liner 101 typically provides for peakenergy absorption in the acoustic frequency range of about between 500and 2000 Hz, and is less effective outside this range. Fan flutter forsuch propulsion systems, however, typically occurs at a lower frequency,depending on the frequency and nodal diameter count of the criticalstructural mode. The structural frequency largely depends on the size ofthe fan, among other design parameters. Large fans tend to flutter atsmaller frequencies than small fans. Torsion modes tend to have higherfrequency than bending modes on any given fan, and either can becritical. The materials and construction techniques used to make the fanblades also have a significant influence on the frequency. Given therange of sizes, materials, and flutter critical modes in fans of moderngas turbine engines, the flutter frequency will typically occur at afrequency range of less than but not equal to 500 Hz, and morespecifically between 50 and 400 Hz, yet more specifically between 50 and300 Hz, and yet more specifically between 50 and 200 Hz.

In one embodiment, a flutter damper 102 is provided which may includethe acoustic liner 101 and a chamber 118 disposed radially exterior toand in acoustic communication with the acoustic liner 101. Also aflutter damper 102 without the acoustic liner 101 is considered part ofthe scope of this disclosure. As used herein, radially refers to theaxis A of the engine 20. Acoustic communication is provided through aperforation section 120 in the outer back sheet 110. In FIG. 2, theflutter damper 102 is illustrated as being disposed between a firstaxial forward nacelle bulkhead 114 and a second axial forward nacellebulkhead 116. The flutter damper 102, however, may be disposed anywherebetween a leading edge 111 of the fan 42 and a nacelle hilite 113, suchas flutter damper 102A disposed on the fan case 115 illustrated in FIG.1.

The flutter damper 102 may be configured to mitigate fan flutter byproviding peak energy absorption in the acoustic frequency rangeassociated with fan flutter modes, where such frequency range isreferred to herein as a flutter frequency range. The flutter damper mayhave desirable impedance characteristics at certain targeted flutterfrequencies, which may be defined as:f _(target) =f _(S,ND) +Q·ND

In the equation above, the variable f_(S,ND) is the frequency, which ismeasured in units of Hertz, and which corresponds to a resonancefrequency of a structural mode of the fan blade, which typically may bea first or second bending mode with a certain nodal diameter count, ND.The variable ND is the nodal diameter count of the circumferentialpattern of the structural mode of the fan blade. The variable Ω is therotational speed of the fan, which is measured in the units ofrevolutions per second. The values for variable Ω may be chosen tocorrespond to conditions where fan flutter may typically occur, forexample, when the tip relative Mach number of the fan is between 0.85and 1.2 during standard-day, sea-level-static operation.

From the above equation, considering the nodal diameter constraints, thetargeted flutter frequency ranges may be defined to be:

-   -   f_(S,ND)=frequency of first or second bending mode of fan with        ND nodal diameters        1≤ND≤3        Ω_(Mreltip=0.85)≤Ω≤Ω_(Mreltip=1.2)        f _(target) =f _(S,ND) +Ω·ND

In the above equation, Mreltip is the tip relative Mach number for aradial outer tip of the fan blade, and the bending mode is a vibrationalmode of the fan blade. The symbol Ω_(Mreltip=0.85) denotes therotational speed where the tip relative Mach number is equal to 0.85;likewise, Ω_(Mreltip=1.2) denotes the rotational speed where the tiprelative Mach number is equal to 1.2, Of course, values greater orlesser than the aforementioned values are considered to be within thescope of the present disclosure.

Within the flutter frequency ranges associated with the first and secondbending mode, and more specifically at the targeted frequencies, theflutter damper may have the following impedance characteristics:R≥2ρc−3ρc≤X≤−0.6ρc

Again, these values may vary and fall within the scope of the presentdisclosure. The above equation references the impedance of the flutterdamper, defined as the complex ratio of the amplitude and phase ofpressure oscillations over the amplitude and phase of the acousticvelocity as a function of frequency. In addition, the equationreferences the real part of impedance is the resistance, which isvariable R, and the imaginary part of impedance is the reactance, whichis variable X. The variable ρ is the air density, and the variable c isthe sound speed, both being at the entrance to the flutter damper. Theresistance constraint on R may facilitate integration of the flutterdamper into acoustic liners, which typically have R values greater than2ρc in locations forward of the fan. The reactance constraint on Xoptimizes the flutter inhibiting capability of the device at operatingconditions typically encountered in commercial aircraft applications. Atcertain target frequencies, the flutter damper may satisfy the followingadditional constraint:

$0.0143 \leq \frac{{Vf}_{target}}{Sc} \leq 0.165$

Again, these values may vary and fall within the scope of the presentdisclosure. As illustrated in FIGS. 3, 4A and 4B, discussed in greaterdetail below, the chamber 118 has a width W, a height H, and a length L.In addition, the perforated section 120 disposed under the chamber 118has a width Wp and a length Lp, and the acoustic liner 101 has a heightH_(Li). Thus, in the above equation, the volume of the flutter damper102, which includes the volume (W×H×L) of chamber 118 and the volume(Wp×H_(Li)×Lp) of the acoustic liner 101 is variable V. The area of theperforated section 120 (Wp×Lp) disposed under the chamber 118 isvariable S. The units of V, S, c and f_(target) are chosen such that

$\frac{{Vf}_{target}}{Sc}$is non-dimensional.

Moreover, in one embodiment, a downstream edge of the chamber 118 may belocated at B/D≤0.35. In this equation, the variable B is the distancebetween the downstream edge of the chamber 118 and the fan tip leadingedge, and the variable D is the fan tip diameter at the leading edge ofthe fan blade.

Remaining with FIGS. 1-3, the illustrated flutter damper 102 designedaccording to the above constraints, has the benefit of being able to fitwithin smaller footprints of sized-optimized propulsion systems,providing a retrofittable solution to an existing engine inlet. Thus thedisclosed flutter damper 102 may help boost fan flutter margin withoutrequiring an inlet redesign. In addition, the flutter damper 102 mayprovide a relatively lightweight solution, that is, the low temperaturesof the inlet area may allow for the use of a metallic material,including aluminum, or a plastic or a composite, or a hybrid metallicand non-metallic material. Moreover, the flutter damper 102 may have ascalable design which can be oriented in an array of chambers, discussedin detail, below, and as illustrated in at least FIG. 5. For example,the array of chambers and may be placed around an engine inletcircumference to achieve a desired amount of flutter dampening volume.

As illustrated in FIG. 4A, the perforation section 120 in the outer backsheet 110 may be rectangular in shape with length Lp and width Wp, wherethe length direction Lp corresponds to the engine axial direction, andthe width direction Wp corresponds to the engine circumferentialdirection. For a contemporary high bypass ratio propulsion system, whichmay have a fan diameter of about 80 inches, and a fan rotor hub-to-tipratio of about 0.3, the length Lp may be about four and half (4.5)inches for the chamber 118, and the width Wp may be about twelve (12)inches for chamber 118. Each perforation section 120 may have ahole-diameter of about thirty thousandths (0.030) of an inch. Of course,dimensions greater or lesser than the aforementioned dimensions areconsidered to be within the scope of the present disclosure. Thisperforation geometry provides an open area that may be about four andhalf (4.5) percent of the surface area (Lp×Wp) of the chamber 118against the outer back sheet 110, which may be the same open area as aperforation section (not illustrated) in the inner face sheet 108.Again, these dimensions may vary and remain within the scope of thepresent disclosure.

The chamber 118 may be sized to optimally dampen fan flutter at aspecific fan flutter frequency and nodal diameter. The nodal diametercount represents the nodal lines of vibrational modes observed for thefan blade, which typically may be between 1 and 3. The chamber 118 inFIG. 2, for example, is shaped as a rectangular box, and may be sizedbased on an observed flutter frequencies and nodal diameters for a givenengine. For example, if an engine has an observable flutter mode at afrequency of about 150 Hz with nodal diameter 2, the chamber 118 may besized according to that flutter mode and nodal diameter.

The box shape, as illustrated in FIG. 4B, may have a top surface 122roughly defined by a width-length (W×L) area, where the length directionL corresponds to the engine axial direction, and the width direction Wcorresponds to the engine circumferential direction. The box shape mayalso have a front surface 124 and a back surface 125, each roughlydefined by a height-width (H×W) area, where the height direction H forthe chamber 118 may correspond to an engine radial direction. The boxshape may further have a side surface 126 roughly defined by aheight-length (H×L) area. Again, these dimensions may vary and remainwithin the scope of the present disclosure.

For the exemplary embodiment, the chamber 118 is twelve (12) incheswide, as referenced above, and the chamber width-height-length (W×H×L)volume may be three hundred twenty four (324) cubic inches, and theheight H may be equal to, or less than, six (6) inches.

Turning now to FIGS. 4A and 4B, the box shaped chamber 118 may have abottom edge 128 that geometrically conforms to the annular and axialprofile shape of the nacelle inlet 103. Extending axially andcircumferentially outwardly from the bottom edge 128 of the chamber 118is a mounting flange 130 for affixing the chamber 118 to an existingnacelle inlet 103. As such, the bottom face 131 of the chamber 118 maybe formed by the radial outer back sheet 110 of the acoustic liner 101.

The chamber 118 may also include first and second stiffening structures132, 134. The stiffening structures 132, 134 may have a substantially“C” shape, when viewing into the side surface 126 of the chamber 118,which protrudes outwardly from the top 122, front 124 and back 125surfaces of the chamber 118. The stiffening structures 132, 134 maydivide the top surface 122 of the chamber 118 in substantially equalportions in the width direction W. The stiffening structures 132, 134may tune the structural resonance frequencies of the chamber 118 awayfrom the fan flutter frequencies to avoid fan flutter inducing resonancein the chamber 118. For example, the stiffening structures 132, 134 maytune the structural resonance frequencies of the relatively large, flattop surface 122 of the chamber 118 out of the targeted flutter frequencyrange. In addition, the stiffening structures 132, 134 add structuralrigidity and may allow for a lightweight design of the chamber 118.

One or more weep holes 136 may be provided to allow for water or fluidegress. The placement of the weep holes 136 is selected to be below theengine centerline

Turning now to FIGS. 5 and 6 a circumferential array 138 of chambers118, including fourteen (14) chambers 118, is disposed about the nacelleinlet 103, with each of the chambers 118 having a perforated section.Disposing the chambers 118 in this type of circumferential array 138achieves a desired damping volume.

Turning now to FIG. 7, illustrated is an intake area of an engine 152,which may include a nose cone 154, a fan having, e.g., a fan blade 156,and a nacelle 158 radially outside of the fan. Between the fan blade 156and the hilite 160, or leading edge, of the nacelle 152 may be a chamber162, functioning as a flutter-inhibiting device, or a plurality ofchambers. The chamber 162 may modify the reflection characteristics ofthe intake at targeted frequencies. The chamber 162 may be located onthe radially inner facing flow path surface, between the hilite 160 anda leading edge 166 of the fan blade 156.

As illustrated in FIGS. 8A-8C, each chamber 162 may consist of one ormore cavities, including, e.g., a first cavity 168 which may be fluidlyconnected to, and may communicate with, the main flow path 164, and asecond cavity 170 that may be fluidly connected to, and radially outsideof, the first cavity 168.

The first cavity 168, which may be radially closer to the main flow path164, may be covered on a flow facing surface 172 of the first cavity168, by a face sheet formed of a permeable structure. The permeablestructure may be formed from a perforated plate, wire or fabric mesh, orother material that allows sound waves to propagate between the mainflow path 164 and the first cavity 168.

The second cavity 170 may be fluidly connected to the first cavity 168through a surface 174 formed by a sheet of similar permeable structureas used for surface 172. Either of the cavities 168, 170 may containcellular structures, such as honeycomb or baffles, to control thedirection of sound propagation of within the cavities.

In one embodiment, illustrated in FIG. 8B, the flutter damper may have aflow facing face sheet 172 that may be a perforated plate. The firstcavity 168 may contain a cellular structure. A second cavity 170 maycontain no cellular structure, and a second sheet 174 separating thefirst cavity 168 and second cavity 170 may be formed from a perforatedplate.

In another embodiment, illustrated in FIG. 8C, the flow facing facesheet 172 may be comprised of the same permeable structure as the facesheet 164 of the surrounding acoustic liner 176. In addition, thecellular structure in the cavity 168 may be comprised of the samecellular structure as that in the surrounding acoustic liner 176.

Applying the above formulae, at certain target frequencies, the flutterdamper may satisfy the following constraints at the flow facing surface172:

R ≥ 2ρ c − 3ρ c ≤ X ≤ −0.6ρ c$0.0143 \leq \frac{{Vf}_{target}}{Sc} \leq 0.165$

Again, these values may vary and fall within the scope of the presentdisclosure. In the above equation, the volume of the flutter damper 162,which includes the volume of cavity 170 and the volume of cavity 168, isvariable V, and the area encompassing the perforations in the secondsheet 174 is the area S. For the exemplary rectangular embodimentpreviously shown in FIGS. 3 and 4, the volume V is equal to W×H×L plusWp×H_(Li)×Lp, and the area S is equal to Lp×Wp. The units of V, S, c andf_(target) are chosen such that

$\frac{{Vf}_{target}}{Sc}$is non-dimensional. As indicated, the flutter damper may be locatedalong the surface 164 of the main flow path, between the hilite 160 andfan tip leading edge 166.

Further, as indicated above, the targeted frequencies for the flutterdamper may be within a frequency range determined by:

-   -   f_(S,ND)=frequency of first or second bending mode of fan with        ND nodal diameters        1≤ND≤3        Ω_(Mreltip=0.85)≤Ω≤Ω_(Mreltip=1.2)        f _(target) =f _(S,ND) +Ω·ND

Again, values for the frequency range may vary and fall within the scopeof the present disclosure.

Moreover, as indicated above, the downstream edge of the flutter damperis located at B/D≤0.35 where the variable B is the distance between thedownstream edge of the flutter damper 162 and the fan tip leading edge166, and the variable D is the fan tip diameter at the leading edge 166of the fan blade 156.

It is within the scope of the disclosed embodiments to dampen differentfrequencies with each chamber 162 of a plurality of chambers 162installed in the nacelle 158.

The term “about” is intended to include the degree of error associatedwith measurement of the particular quantity based upon the equipmentavailable at the time of filing the application. For example, “about”can include a range of ±8% or 5%, or 2% of a given value.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the presentdisclosure. As used herein, the singular forms “a”, “an” and “the” areintended to include the plural forms as well, unless the context clearlyindicates otherwise. It will be further understood that the terms“comprises” and/or “comprising,” when used in this specification,specify the presence of stated features, integers, steps, operations,elements, and/or components, but do not preclude the presence oraddition of one or more other features, integers, steps, operations,element components, and/or groups thereof.

While the present disclosure has been described with reference to anexemplary embodiment or embodiments, it will be understood by thoseskilled in the art that various changes may be made and equivalents maybe substituted for elements thereof without departing from the scope ofthe present disclosure. In addition, many modifications may be made toadapt a particular situation or material to the teachings of the presentdisclosure without departing from the essential scope thereof.Therefore, it is intended that the present disclosure not be limited tothe particular embodiment disclosed as the best mode contemplated forcarrying out this present disclosure, but that the present disclosurewill include all embodiments falling within the scope of the claims.

What is claimed is:
 1. An acoustic liner for a nacelle inlet of a gasturbine engine, comprising: a flutter damper comprising: acircumferential array of chambers disposed about the acoustic liner,wherein a flutter dampening volume includes a volume of thecircumferential array and a volume of the acoustic liner, each of thechambers including: a first cavity having a radially inner side in fluidcommunication with a flow path, the first cavity extending rapidlyoutwardly from the acoustic liner, and a second cavity having a radiallyinner side in fluid communication with a radially outer side of thefirst cavity, the second cavity having an arcuate profile and a largervolume than the first cavity; and the flutter damper having an impedancecharacteristic at one or more target frequencies defined as:f _(target) =f _(S,ND) +Ω·ND wherein f_(S,ND) is a resonance frequencycorresponding to a structural mode of a rotating component; ND is anodal diameter count of the structural mode; and Ω is a rotational speedof the rotating component; and wherein the flutter damper has thefollowing impedance characteristic at the one or more targetedfrequencies:R≥2ρc−3ρc≤X≤−0.6ρc wherein R is the real part of the impedancecharacteristic, X is the imaginary part of the impedance characteristic,ρ is air density, and c is speed of sound.
 2. The liner of claim 1,wherein the rotating component is a fan blade, and the targetedfrequencies include: f_(S,ND)=frequency of first or second bending modeof fan with ND nodal diameters1≤ND≤3Ω_(Mreltip=0.85)≤Ω≤Ω_(Mreltip=1.2) wherein Mreltip is a relative Machnumber for a radial outer tip of the fan blade, and the bending mode isa vibrational mode of the fan blade.
 3. The liner of claim 2, wherein atthe one or more target frequencies:$0.0143 \leq \frac{{Vf}_{target}}{Sc} \leq 0.165$ wherein V is acombined volume of the first and second cavities, and S is an entrancearea to the second cavity.
 4. The liner of claim 3, wherein the firstcavity and the flow path surface fluidly communicate through a firstperforated surface, and the first cavity and second cavity fluidlycommunicate through a second perforated surface.
 5. The liner of claim4, wherein the first cavity contains a cellular structure.
 6. The linerof claim 5, wherein the first cavity has a smaller volume than thesecond cavity.
 7. The liner of claim 5, wherein the first cavity is anacoustic liner for a propulsion system.
 8. A gas turbine propulsionsystem, comprising: a nacelle; an acoustic liner for a nacelle inlet ofthe nacelle; a flutter damper for a rotating component secured in thenacelle and disposed proximate a flow path, the flutter dampercomprising: a circumferential array of chambers disposed about theacoustic liner, wherein a flutter dampening volume includes a volume ofthe circumferential array and a volume of the acoustic liner, each ofthe chambers including: a first cavity having a radially inner side influid communication with a flow path, the first cavity extendingradically outwardly from the acoustic liner, and a second cavity havinga radially inner side in fluid communication with a radially outer sideof the first cavity, the second cavity having an arcuate profile and alarger volume than the first cavity; and the flutter damper having animpedance characteristic at one or more target frequencies defined as:f _(target) =f _(S,ND) +Ω·ND wherein f_(S,ND) is a resonance frequencycorresponding to a structural mode of a rotating component; ND is anodal diameter count of the structural mode; and Ω is a rotational speedof the rotating component; and wherein the flutter damper has thefollowing impedance characteristic at the one or more targetedfrequencies:R≥2ρc−3ρc≤X≤−0.6ρc wherein R is the real part of the impedancecharacteristic, X is the imaginary part of the impedance characteristic,ρ is air density, and c is speed of sound.
 9. The gas turbine propulsionsystem of claim 8, wherein the rotating component is a fan blade, andthe targeted frequencies include: f_(S,ND)=frequency of first or secondbending mode of fan with ND nodal diameters1≤ND≤3Ω_(Mreltip=0.85)≤Ω≤Ω_(Mreltip=1.2) wherein Mreltip is a relative Machnumber for a radial outer tip of the fan blade, and the bending mode isa vibrational mode of the fan blade.
 10. The gas turbine propulsionsystem of claim 9, wherein at the one or more target frequencies:$0.0143 \leq \frac{{Vf}_{target}}{Sc} \leq 0.165$ wherein V is acombined volume of the first and second cavities, and S is an entrancearea to the second cavity.
 11. The gas turbine propulsion system ofclaim 10, wherein the first cavity and the flow path surface fluidlycommunicate through a first perforated surface, and the first cavity andsecond cavity fluidly communicate through a second perforated surface.12. The gas turbine propulsion system of claim 11, wherein the firstcavity contains a cellular structure.
 13. The gas turbine propulsionsystem of claim 10, wherein the first cavity has a smaller volume thanthe second cavity.
 14. The gas turbine propulsion system of claim 10,wherein the first cavity is an acoustic liner for a propulsion system.15. A method of providing flutter damping to a gas turbine engine,comprising: passing a flow over a flutter damper of an acoustic linerfor a nacelle inlet of a nacelle, the flutter damper having acircumferential array of chambers disposed about the acoustic liner,wherein a flutter dampening volume includes a volume of thecircumferential array and a volume of the acoustic liner, each of thechambers including: a first cavity with a radially inner side in fluidcommunication with a flow path surface, the first cavity extendingradially outwardly from the acoustic liner, and a second cavity having aradially inner side in fluid communication with a radially outer side ofthe first cavity, the second cavity having an arcuate profile and alarger volume than the first cavity; and dampening flutter for arotating component disposed in a flow path with the flutter damper atone or more target frequencies defined as:f _(target) =f _(S,ND) +Ω·ND wherein f_(S,ND) is a resonance frequencycorresponding to a structural mode of the rotating component, ND is anodal diameter count of the structural mode, and Ω is a rotational speedof the rotating component; and wherein the flutter damper has thefollowing impedance characteristic at the one or more targetedfrequencies:R≥2ρc−3ρc≤X≤−0.6ρc wherein R is the real part of the impedancecharacteristic, X is the imaginary part of the impedance characteristic,ρ is air density, and c is speed of sound.
 16. The method of claim 15,wherein the rotating component is a fan blade, and the targetedfrequencies include: f_(S,ND) frequency of first or second bending modeof fan with ND nodal diameters1≤ND≤3Ω_(Mreltip=0.85)≤Ω≤Ω_(Mreltip=1.2) wherein Mreltip is a relative Machnumber for a radial outer tip of the fan blade, and the bending mode isa vibrational mode of the fan blade.